Generic hyperbolic knot complements without hidden symmetries

TL;DR

This paper develops criteria to identify hyperbolic knot complements without hidden symmetries, using rational functions on link varieties, and applies these to infinite families of knots.

Contribution

It introduces new criteria based on rational functions to determine the absence of hidden symmetries in hyperbolic knot complements.

Findings

Most knot complements in certain families lack hidden symmetries

Criteria successfully applied to infinite families of knots

Finitely many exceptions identified

Abstract

We establish a pair of criteria for proving that most knot complements obtained as Dehn fillings of a given two-component hyperbolic link complement lack hidden symmetries. To do this, we use certain rational functions on varieties associated to the link. We apply our criteria to show that among certain infinite families of knot complements, all but finitely many members lack hidden symmetries.